Introduction to Optical Components

Roshan L. Aggarwal, Kambiz Alavi

• Publisher: CRC Press
• Year: 2018
• eBook ISBN: 9781351189491
• Edition: 1
• Topic: Technology & Engineering
• Subtopic: Electrical Engineering & Telecommunications
• Index: Technology & Engineering

"This book provides a practical description of optics that satisfies the needs often encountered by some engineers in the practice of their profession. Optical components, including optical sources and detectors, have found their way into products that we buy for the house, and into industrial equipment. As a textbook, it provides an efficient tool for the student to gain in-depth knowledge of a subject, with homework problems to test and verify mastery of the subject."
— Antonio Sanchez-Rubio, MIT Lincoln Laboratory, Lexington, Massachusetts, USA

"This book covers all the experimental tools, described meticulously and with clear illustrations, which students will need to perform their experiments. I wish I had this book when I taught an optics course!"
— A.K. Ramdas, Purdue University, West Lafayette, Indiana, USA

This book provides readers with a brief introduction to optical components. Materials presented in this book prepare readers to deal with optical components in the areas of optics and optical technology. Introduction to Optical Components features nine chapters with topics ranging from lenses (materials, magnifiers, and cameras); mirrors (spherical, ellipsoidal, and aberrations); diffraction gratings (holographic and multilayer dielectric); polarizers (birefringent, reflective, and Jones matrix algebra); windows (UV and AR coating materials); filters (neutral density and Raman); beamsplitters (plate, cube, and pellicle); sources (light-emitting diodes and lasers); and detectors (thermal, photon, and photodetector noise). This text also features a detailed discussion of non-ideal effects for practical components using minimal amounts of derivations (that do not compromise essential physical, mathematical, or material properties). While there are numerous books that feature "optical" in their title, to date, no textbook on optical components exists. It is for this reason that Introduction to Optical Components is such a vital resource. The technical level of this book is equivalent to an undergraduate course in the optics and optical technology curriculum. Students are required to have little familiarity with optics. Practitioners in optics and optical technology will also find this book useful. Each chapter includes numerous mathematical equations; tables providing useful optical parameters for many optical materials; and end-of-chapter questions and their corresponding solutions.

1

Lenses

1.1 INTRODUCTION

The earliest known lenses date back to 750 BC, and were made from polished crystal, often quartz. One such example of an ancient lens in the collection of the British Museum (#90959) was ground and polished with one plane surface and one slightly convex surface. Lenses are commonly used as magnifiers for viewing small objects. Lenses are also used in optical systems such as binoculars, cameras, eyeglasses, microscopes, telescopes, and other optical systems. For additional information on lenses, the following books are recommended: Fowles (1975); Hecht and Zajac (1974); Jenkins and White (1976).

There are six types of lenses: biconvex, plano-convex, positive meniscus, negative meniscus, plano-concave, and biconcave, as shown in Figure 1.1.

We now consider a biconvex lens of refractive index n, diameter D, focal length f, front focal length f_F, and back focal length f_B located in a medium of refractive index of 1.0 (vacuum or air). Figure 1.2 shows a thick lens with radii of curvature R₁ and R₂ for the two lens surfaces, and center thickness t_C.

The optical axis of the lens (C₂C₁) intersects the two surfaces of the lens at points V₁ and V₂. V₁V₂ is equal to t_C. C₁ and C₂ denote the centers of curvature of the two lens surfaces. V₁C₁ is equal to R₁. V₂C₂ is equal to R₂. F₁ and F₂ denote the front and back focal points of the lens. H₁ and H₂ denote the primary and secondary principal planes, respectively. An object ray, propagating parallel to the optical axis to the right, is considered to continue through the lens up to the principal plane H₂ and then passes through the back focal point F₂. The distance F₁H₁ or H₂F₂ is equal to the focal length f. The distance F₁V₁ is equal to the front focal length f_F. The distance V₂F₂ is equal to the back focal length f_B. The distances V₁H₁ and V₂H₂ are given by (Fowles 1975).

$V_1{H}_1={\text{δ}}_1=-f{t}_C\left(\frac{n-1}{n{R}_2}\right)$

(1.1)

$V_2{H}_2={\text{δ}}_2=-f{t}_C\left(\frac{n-1}{n{R}_1}\right)$

(1.2)

Distances V₁C₁, V₂C₂, V₁H₁, V₂H₂, F₁H₁, and H₂F₂ are positive if they point to the right, and negative if they point to the left. As shown in Figure 1.2, R₁ is positive, R₂ is negative, δ₁ is positive, and δ₂ is negative. The edge thickness of the lens is given by

$t_E\approx t_C-\frac{D^2}{8}\left(\frac{1}{R_1}-\frac{1}{R_2}\right)$

(1.3)

FIGURE 1.1 Six types of lenses.

FIGURE 1.2 Thick lens with center thickness t_C.

In the paraxial approximation, focal length f is given by

$\frac{1}{f}=(n-1)\left[\frac{1}{R_1}-\frac{1}{R_2}+\frac{\left(n-1\right)t_C}{n{R}_1{R}_2}\right]$

(1.4)

Front focal length f_F is given by

$f_F=f-{\text{δ}}_1$

(1.5)

Back focal length f_B is given by

$f_B=f+{\text{δ}}_2$

(1.6)

Effective focal length of a combination of two thin lenses of focal lengths f₁ and f₂ separated by a distance d is given by

$\frac{1}{f}=\frac{1}{f_1}+\frac{1}{f_2}-\frac{d}{f_1{f}_2}$

(1.7)

Back focal length for this combination of the two lenses is given by

$f_B=f\left(1-\frac{d}{f_1}\right)$

(1.8)

Location of the f lens on the left-hand side of the f₂ lens is given by

$L_f^{f_2}=f\frac{d}{f_1}$

(1.9)

Figure 1.3 shows a plane parallel beam of light incident upon a biconvex lens.

All the light rays pass through the focal spot and then diverge. The diameter of the focal spot is determined by the diffraction of light and the quality of the lens. For a perfect lens, the back focal spot F₂ consists of a bright spot known as the Airy disc, which is surrounded by rings. Eight-four percent of the light goes into the Airy disc and 16% into the rings. The diameter of the Airy disc is equal to 1.22fλ/D, where λ is the wavelength of light and D is the diam...

Table of contents

• Cover
• Half Title
• Title Page
• Copyright Page
• Dedication
• Table of Contents
• Preface
• Acknowledgments
• Authors
• Chapter 1 Lenses
• Chapter 2 Mirrors
• Chapter 3 Diffraction Gratings
• Chapter 4 Polarizers
• Chapter 5 Optical Windows
• Chapter 6 Optical Filters
• Chapter 7 Beamsplitters
• Chapter 8 Light Sources
• Chapter 9 Light Detectors
• Appendix
• References
• Index